Rogue waves of the AB system on the periodic background

Abstract

In this paper, we study rogue wave solutions of the [Formula: see text] system under the background of Jacobian elliptic functions. First, we introduce the Jacobian elliptic functions dn and cn through traveling wave transformation. Next, we derive the expression of spectral parameters [Formula: see text] and rogue wave with periodic background by nonlinearization of the Lax pair and the Darboux transformation (DT) method. At last, we present the dynamic evolution process of the [Formula: see text] system in some figures.